Order of Operations – Definition with Examples

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What is Order of Operations?

In math, order of operations are the rules that state the sequence in which the multiple operations in an expression should be solved.

A way to remember the order of the operations is PEMDAS, where in each letter stands for a mathematical operation.

 P Parentheses
 E Exponent
 M Multiplication
 D Division
 A Addition
 S Subtraction

The PEMDAS rules that state the order in which the operations in an expression should be solved, are:

1. Parentheses – They take precedence over all other operators. The first step is to solve all the operations within the parentheses. Work out all groupings from inside to out. (Whatever is in parentheses is a grouping)

2. Exponents – Work out all the exponential expressions. 

3. Multiplication and Division – Next, moving from left to right, multiply and/or divide whichever comes first.

4. Addition and Subtraction – Lastly, moving from left to right, add and/or subtract whichever comes first.

Order of Operations in expressions PEMDAS


Why Follow Order of Operations?

 Follow the rules of the order of operations to solve expressions so that everyone arrives at the same answer. 

Here’s an example of how we can get different answers if the correct order of operations is NOT followed.

Expression solved from Left to RightExpression solved using Order of Operations (PEMDAS)
6 x 3 + 4 x ( 9 ÷ 3 )6 X 3 + 4 x ( 9 ÷ 3 )18 + 4 x ( 9 ÷ 3 )22 x ( 9 ÷ 3 )198 ÷ 3= 66     ✘6 x 3 + 4 x ( 9 ÷ 3 )6 X 3 + 4 x ( 9 ÷ 3 ) → P6 X 3 + 4 x 3 → M18 + 4 x 3 → M18 + 12 → A= 30     ✔
Fun Fact:
A popular mnemonic used to remember the order of operations -PEMDAS is ‘Please Excuse My Dear Aunt Sally’. 

Let’s sing!

It’s all really about the operations,
Solve in order, else there’ll be tensions.
Start by opening the Parentheses.
Jump up with the Exponents.
Cube or Square – it’s all very fair!
Next, Multiply or Divide – jus’ go left to right.
Add or Subtract come last but they’re easy.
finally, it’s as simple as A B C D!

Let’s do it!

Instead of handing out practice worksheets to your child, form word problems from real life situations. This will help them write and solve expressions and use the order of operations to simplify expressions in pre-algebra and algebra. For instance, take your child out for shopping. Ask them to pick out 2 dozen eggs, 3 packets of hot dog buns, 2 packets of candy and 2 boxes of cereal. Then, ask them to put one box of cereal back. Now, ask your child the number of eggs in a dozen, number of buns in a packet, number of candies in a packet and calculate the total number of items bought. Ask them to form an expression and use the order of operations to find the answer. 

Expression

Practice Problems

Order of Operations

Attend this Quiz & Test your knowledge.

1What will be the first step in evaluating the following expression: $(3 + 7) – 2 × 5 – 9 ÷ 3$

Division
Multiplication
Subtraction
Addition
CorrectIncorrect
Correct answer is: Addition
When evaluating math expressions, order of operations is followed as Parentheses - Exponents, Division, Multiplication, Addition, and Subtraction (PEMDAS).
Therefore, the first step would be to evaluate (3 + 7), i.e., adding the numbers inside the parentheses.

2[(28 ÷ 4) + 3] × 2 = ___

20
22
18
13
CorrectIncorrect
Correct answer is: 20
When evaluating math expressions, order of operations is followed as Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction (PEMDAS).
$[(28 ÷ 4) + 3] × 2 = [7 + 3] × 2 = 10 × 2 = 20$

34 ÷ 4 + 2 × 2 = ___

6
5
3
4
CorrectIncorrect
Correct answer is: 5
When evaluating math expressions, order of operations is followed as Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction (PEMDAS).
$4 ÷ 4 + 2 × 2 = (4 ÷ 4) + (2 × 2) = 1 + 4 = 5$

49 – 6 ÷ 3 = ___

1
9
7
0
CorrectIncorrect
Correct answer is: 7
When evaluating math expressions, order of operations is followed as Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction (PEMDAS). So, $9 – 6 ÷ 3 = 9 – (6 ÷ 3) = 9 – 2 = 7.$

Frequently Asked Questions

In math, order of operations is the rules of the sequence in which the multiple operations in an expression should be solved.

In math, we follow the order of operations rules to solve expressions so that everyone arrives at the same correct answer.

PEMDAS is a way to remember the order of the operations, where each letter stands for a mathematical operation. P stands for Parentheses, E stands for Exponent, M stands for Multiplication, D stands for Division, A stands for Addition, and S stands for Subtraction. If there are two or more operations in a single expression, the order of the letters in PEMDAS tells what to calculate first, second, third, and so on until the calculation is complete.

2 + 3 x 4 is 14. According to the PEMDAS rule, we multiply before adding. So the first step in solving 2 + 3 x 4 is to multiply 3 by 4, and then add 2 to the product. So, 2 + 3 x 4 = 2 + 12 = 14.


Order of Operations – Definition with Examples

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